Arrangements of lines with a minimum number of triangles are simple

Abstract

Levi has shown that for every arrangement of n lines in the real projective plane, there exist at least n triangular faces, and Grünbaum has conjectured that equality can occur only for simple arrangements. In this note we prove this conjecture. The result does not hold for arrangements of pseudolines. © 1988 Springer-Verlag New York Inc.